Additive Synthesis

A synthesiser isn't an acoustic instrument, so to achieve a sound more complex than a basic VCO waveform that is still musically pleasing, harmonics will be introduced - whether by shaping the basic waveform or combining multiple waveforms.The easiest way to achieve this extra complexity is to mix multiple sinewaves together in a harmonically consistent way - this is the basis of additive synthesis.

Let's consider a real sound such as a plucked string. We know from experience that this is loud and bright at the start of the note, and becomes quieter and "darker" as time passes. So let's take this simplistic description and see how we can modify a synth to recreate these tonal changes.


 * first we must assign the pitches of the oscillators to imitiatethe harmonic nature of the string (This is the simple harmonic series).
 * Second, we must consider how each of these harmonics change in time. this is also simple: we know that the sound becomes duller as time passes, so the higher-fgrequency harmonics must decay more rapidly than the lower ones.
 * third, we must determine how the overall brightness and loudness of the sound changes as the note progresses, and create filter and VCA profiles that emulate this.

envelope shapes diagram for each wave

there is a 'but' though: since an additive sound with multiple harmonics can be thought of as all the different pitches and amplitudes of these harmonics (i.e. a comlex sound is made of multiple musically pleasing pitches with different amplitudes), it turns out there is no need for these filters and amplifiers - the changes in the harmonics can do all the work. even though an additive synth patch lacks the filters and output VCA of a conventional east-coast patch, it is still capable of creating most of the timbres of a typical VCO-VCF-VCA configuration.

diagram of combined waveform

Back to the plucked string sound, lets say that VCO 1 produces a sinewave at the fundamental (1st harmonic) frequency, VCO 2 produces a sine wave at the second harmonic frequency, and so on. If each VCO has an enveloped VCA to shape it and so, for example, the sound of VCO 1 takes time to decay from its full level to silence, and the enveloped VCA for VCO 2 causes the sound of VCO 2 to decay from it's maximum level to silence in half that time, and so on, then these relationships mean that the higher harmonics are louder at the start, so this sound is particularly bright in the first instance, much like a plucked or hammered string. Also, because the higher frequencies are decaying more quickly, the sound becomes 'darker' as time passes - if you look at the time that the waveform, it can be seen that the high frequencies decay quickly and that, by the time that the decays to silence, only the fundamental remains.

This is a very simple way to generate complex buit musically pleasing waveforms - but, the problem is that it requires many VCOs, each with it's own enveloped VCA and hence also multiples, buffered multiples and large num,bers of extra modules to add any further shaping or filtering to the sound. How do we get more complex sounds wiothout an immense number of modules? The answer is in shaping the fundamental waveforms themselves to produce extra harmonics, i.e. 'modulating' the sources of the waveforms - the oscillators.

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